A fixed, timing-based radio positioning system may consist of a set of ranging transmitters (e.g., Tx1 to Txn) such that a receiver capable of receiving such transmissions can estimate its position. The accuracy of a receiver's position estimate is negatively affected by multiple factors, including: resolution of the transmission signal; synchronization of the transmitters; presence of reflected signals, resulting in the over-estimation of a range between the receiver and a transmitter; uncertainty about the estimated velocity and range of the receiver with respect to any given transmitter due to noise, insufficient signal strength or other radio properties; and poor geometry among the transmitters relative to the receiver, which increases the uncertainty of the position determined using the range from a given transmitter set with poor angular separation among them.
The above characteristics result in a combination of fixed range error biases and fixed range uncertainty functions at any given estimated point within the real plane. That is, a building causing a reflection creates a fixed reflection. An error in synchronization between two transmitters is a fixed error between those two transmitters, within the stability of the synchronization system. Poor geometry or bandwidth-related resolution limits will result in position bias with a fixed histogram based on the geometric properties of the network. These biases are endogenous to the radio positioning system.
Accordingly, if biases can be detected, and the uncertainty of a given range estimate can be reduced, then the quality of position can be improved. With known locations of transmitters, the physical and geometric properties of the transmitter network could enable considerable improvements compared to techniques applied to networks where there is less information about the network. Further, knowledge about the biases detected may be propagated through an error-correction system due to the fixed nature of the radio positioning system and the fixed nature of the biases.